Become a MacRumors Supporter for $50/year with no ads, ability to filter front page stories, and private forums.
It wil run fine with 256 MB of RAM. I'm running 10.3.9 on an iMac G3 500 MHz with 128 MB RAM (the minimum requirement of Panther), and it's fine, but it certainly isn't fast. Tiger would probably be slow on your system because 256 MB RAM is the minimum of Tiger, and 350 MHz isn't the fastest, but it will work.
 
Well, to be honest, my 500 MHz iMac G3 on Panther was/is really only good for web browsing, and that's pretty much it. Other tasks are do-able, but certainly not fast. However, you do have more RAM than me, so it may not be that bad.
 
I run Tiger on my 400mHz B&W and it is definitely usable. I would really look to upgrade the RAM though. I have 512mb and it is choppy but overall usable. I say go for it!
 
Im probably going to sell the b&W soon and get a Macbook or a Mac Mini. Im just using this B&W because it was givin to me and I want to see what Mac is like. Ive been a long PC user.
 
I find that as long as you have a lot of RAM, an old mac can seem pretty zippy. Look at my specs below, and I can tell you that although it can get bogged down at times, it's perfect for Webrowsing, emails and light photoshopping (basically the bulk of my work).
 
Register on MacRumors! This sidebar will go away, and you'll see fewer ads.